It would have been fascinating to have been a fly on the wall when Mr Boris Johnson called Mr Donald Trump's special adviser and son-in-law Jared Kushner to express Mrs Theresa May's concern about the US policy which is being widely referred to as the "Muslim ban".
What sort of language did the British Foreign Secretary adopt?
How high were the stakes vis-a-vis the "special relationship" which only 24 hours ago had been reaffirmed by the US President and the British Prime Minister?
We may have to wait for an answer until Mr Johnson publishes his memoirs. Even then, details of what actually happens between diplomats behind closed doors or over a secure phone line are notoriously hard to discover.
But history has given us a few examples where emotions ran high during meetings.
According to some reports, Iranian Foreign Minister Javad Zarif shouted at then US Secretary of State John Kerry so frequently during meetings in 2014 over the nuclear deal with Iran that bodyguards were on standby to intervene. Conservative blogs in the US interpreted it as a sign of weakness that Mr Kerry simply endured the alleged rants.
But remaining calm under pressure can be a powerful resource in negotiations.
Appearances do not necessarily tell us anything about substance.
By contrast, the infamous meeting between Adolf Hitler and Neville Chamberlain in Munich in September 1938 is said to have been conducted in a relatively amicable atmosphere.
Chamberlain considered the preservation of peace of paramount importance and believed that it could be negotiated by conceding to Hitler's demands.
Rarely has there been a more catastrophic assessment of intention and capability of the opposing side in negotiations, particularly given what each side knew about the other's political ideology.
You may have expected Mr Jimmy Carter, a Democrat president, and West German social-democratic chancellor Helmut Schmidt in the 1970s and early 1980s to get on well with each other, given their shared values.
But when they met during the economic summit in Venice in 1980, the situation came close to a physical altercation in a small hotel room. According to a contemporaneous report: "The President (Carter) was very calm but firm throughout and the Chancellor became less aggressive after the clash over Senator Biden's report." This may come as a surprise, as Mr Schmidt presented himself to the outside world as a rational and self-controlled politician. Mr Carter's memoirs, by contrast, describe Mr Schmidt as a "paranoid child".
The value of such stories is not merely anecdotal. They tell us about the importance of using and controlling emotion for international negotiations and diplomacy.
An assessment of the other party's likely reactions frequently forms part of the background briefings for diplomats and politicians on state visits. For example, a portrait of the Soviet leader Nikita Khrushchev that the Central Intelligence Agency prepared for John F. Kennedy in May 1961 warned the US president of Khrushchev's short fuse.
Khrushchev was, the assessment argued, "immoderately sensitive to slights" and was also prone to the "crudest form of barnyard humour" - which would give him something in common with the current occupant of the White House.
Why does this matter? There are two aspects. First, anticipating how the other side might react is crucial in negotiations.
This is why the diplomatic teams plan every aspect of the meeting, from position and background papers, to interpreters, to seating arrangements, to food and drink, in great detail.
And heads of state and their senior negotiators need to be able to understand the best buttons to press in order to exert the desired pressure. This is not always achieved with words - Mr Vladimir Putin famously disconcerted German Chancellor Angela Merkel by releasing his large black Labrador during a meeting - with a photographer conveniently around to capture the scene - a unique way of exerting psychological power.
What does this mean for our understanding of the negotiations between Mr Trump and Mrs May?
One does not have to be a supporter of either to find some of the initial criticism of Mrs May's handling of the visit a bit premature.
This visit was most likely one designed for both parties to get to know each other on a personal level rather than one aimed at any policy agreements. Those who criticised the Prime Minister for a lack of backbone towards Mr Trump are overlooking this.
But Mrs May's supporters must also have been at least a bit embarrassed: Almost immediately after a carefully choreographed visit that showed Mr Trump holding hands with the Prime Minister, he signed an executive order banning people from seven Muslim countries, including those with visas and green cards, from entering the US.
What message did this send to the Prime Minister who had just days before enthusiastically extolled the values the two countries have traditionally shared in a speech to Republican politicians? By symbolically holding hands with him, Mrs May now seems shackled to Mr Trump's domestic policy agenda.
She will not thank him for that.
•The writer is Professor in Contemporary European History, University of Stirling.
•This article first appeared in theconversation.com, a website of analysis from academics and researchers.
A version of this article appeared in the print edition of The Straits Times on February 03, 2017, with the headline 'Handshakes or punches? What goes on behind closed diplomatic doors'. Print Edition | Subscribe
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